There are several options that very in flexibility, cost, difficulty etc.
My preferred method is to use a Pi Cobbler and a PermaProto Board from Adafruit. You could prototype with a breadboard and then transfer the components to the protoboard and solder the connections to make it more permanent (note there are more suppliers for these parts besides Adafruit, also I linked to the full size protobaord but it does come in smaller sizes).
You could carefully solder wire to the GPIO pins themselves - though I would not recommend this.
You could wirewrap the connections (this is the old school method and requires a special tool.
You could create a custom PCB, (either make it yourself or have it manufactured by a company like OSH Park) (when having it made this usually requires a minimum number of boards to be purchased and can be daunting for someone who has not done it before.
Depending on the environment you could just leave it on a breadboard with jumper wires.